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We establish local well-posedness of the Hall-magneto-hydrodynamics(Hall-MHD) system in the Sobolev space $\left(H^s(\mathbb{R}^n)\right)^2$ with$s>\frac n2$. The previously known local well-posedness space was$\left(H^s(\mathbb{R}^n)\right)^2$ with $s>\frac n2+1$. Thus the resultpresented here is an improvement.

Local well-posedness of the Hall-MHD system in $H^s(\mathbb {R}^n)$ with $s>\frac n2$